Any sport is good for your health. I like cycling and I do it very often. I used to ride only in the city, but now I want to ride in the woods close to home. I don't think my bike is suitable for that. Maybe you can advise me on a bicycle for riding in the countryside?
I think that you need to buy one bike that will be suitable for the city and for nature. Go to a store and consult with a salesperson. I think he can help you make the right choice. If you don't have time for that, I recommend reading specialized bike reviews. Remember it's difficult to choose the right bike.